Finite Group Databasebeta

← C5×#18538 #11941258

Subgroups — C5×#18538 #11941258

Order 1280.

922 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3482C211yesmaximal, characteristic
2C5×#3139C211yesmaximal, characteristic, complemented
3C5×#3079C211yesmaximal, characteristic, complemented
4C5×#3079C211yesmaximal, characteristic, complemented
5C5×#1638C212yesmaximal, complemented
6C5×#1637C212yesmaximal, complemented
7C5×#1636C212yesmaximal, complemented
8C5×#1635C212yesmaximal, complemented
9C5×#1561C211yesmaximal, characteristic, complemented
10C5×#1489C211yesmaximal, characteristic, complemented
11C5×#1489C211yesmaximal, characteristic, complemented
12C5×#557C2211yescharacteristic
13C5×#556—21no—
14C5×#556C2211yescharacteristic
15C5×#552—22no—
16C5×#552—21no—
17C5×D4×Q8C2211yescharacteristic
18C5×#548—21no—
19C5×#547—21no—
20C5×#547C2211yescharacteristic
21C5×#533—21no—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529—21no—
25C5×#529—22no—
26C4×C5×#41—21no—
27C4×C5×#41C2211yescharacteristic
28C4×C5×#41C2211yescharacteristic
29C2×C4×C5×Q8—21no—
30C5×#491—22no—
31C5×#487C2212yes—
32C5×#487C2212yes—
33C5×#477C2212yes—
34C5×#477C2212yes—
35C5×#476C2212yes—
36C5×#476C2212yes—
37C5×#475—21no—
38C5×#475—21no—
39C5×#474—21no—
40C5×#474—21no—
41C5×#428—21no—
42C5×#428—21no—
43C5×#423C2211yescharacteristic
44C5×#423C2211yescharacteristic
45C5×#419—22no—
46C5×#417—21no—
47C5×#417—21no—
48C4×C5×M16C2211yescharacteristic
49C5×#332C2212yes—
50C5×#332C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×D4⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18538C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C2×C5×#41D411yescharacteristic
58C2×C5×#41D411yescharacteristic
59C22×C5×Q8—21no—
60C22×C5×Q8—21no—
61C2×C5×M16—21no—
62C2×C5×M16—21no—
63C2×C5×M16—21no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8C2312yes—
70C5×C4⋊Q8C2311yescharacteristic
71C5×C4⋊Q8C2311yescharacteristic
72C5×#126—22no—
73C5×#126—22no—
74C5×#126—22no—
75C5×#125—22no—
76C5×#125—22no—
77C5×#125—21no—
78C5×#125D412yes—
79C5×#124—22no—
80C5×#124—21no—
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—21no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—21no—
91C5×#121—22no—
92C5×#121—21no—
93C4×C5×Q8—22no—
94C4×C5×Q8—22no—
95C4×C5×Q8—21no—
96C4×C5×Q8—21no—
97C4×C5×Q8—21no—
98C4×C5×Q8—21no—
99C4×C5×Q8—21no—
100C4×C5×Q8D411yescharacteristic
101C4×C5×Q8D411yescharacteristic
102C4×C5×Q8C2311yescharacteristic
103C4×C5×Q8C2311yescharacteristic
104C4×C5×D4—22no—
105C4×C5×D4—22no—
106C4×C5×D4—21no—
107C4×C5×D4—21no—
108C4×C5×D4—21no—
109C4×C5×D4—21no—
110C4×C5×D4—21no—
111C4×C5×D4D411yescharacteristic
112C4×C5×D4D411yescharacteristic
113C4×C5×D4C2311yescharacteristic
114C4×C5×D4C2311yescharacteristic
115C5×#117—22no—
116C5×#117—22no—
117C5×#117—21no—
118C5×#117—21no—
119C5×#117—21no—
120C5×#117D412yes—
121C5×#117D411yescharacteristic
122C5×#117D411yescharacteristic
123C2×C5×C4⋊C4—22no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—21no—
127C2×C42×C5—22no—
128C2×C42×C5—21no—
129C2×C42×C5—21no—
130C2×C42×C5C2311yescharacteristic
131C5×#107—22no—
132C5×#107—22no—
133C5×#106—22no—
134C5×#106—22no—
135C5×C4⋊C8—21no—
136C5×C4⋊C8—21no—
137C5×C4⋊C8C2312yes—
138C5×C4⋊C8C2312yes—
139C5×#103—22no—
140C5×#103—22no—
141C5×#103—24no—
142C5×#103—24no—
143C5×#102—22no—
144C5×#102—22no—
145C5×#97—21no—
146C4×C5×C8C2312yes—
147#3482C2×C511yescharacteristic
148#3139C2×C511yescharacteristic, complemented
149#3079C2×C511yescharacteristic, complemented
150#3079C2×C511yescharacteristic, complemented
151#1638C2×C512yescomplemented
152#1637C2×C512yescomplemented
153#1636C2×C512yescomplemented
154#1635C2×C512yescomplemented
155#1561C2×C511yescharacteristic, complemented
156#1489C2×C511yescharacteristic, complemented
157#1489C2×C511yescharacteristic, complemented
158C5×#41—22no—
159C5×#41—22no—
160C5×#41—41no—
161C5×#41—41no—
162C5×#41—42no—
163C5×#41—42no—
164C2×C5×Q8—22no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—22no—
168C2×C5×Q8—44no—
169C2×C5×Q8—42no—
170C2×C5×Q8—42no—
171C2×C5×Q8—41no—
172C2×C5×Q8C2×D411yescharacteristic
173C2×C5×Q8C2×D411yescharacteristic
174C2×C5×D4—22no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4C2×D411yescharacteristic
178C2×C5×D4C2×D411yescharacteristic
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—41no—
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C5×M16—42no—
192C5×M16—42no—
193C5×M16—42no—
194C2×C5×C8—22no—
195C2×C5×C8—22no—
196C2×C5×C8—22no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—41no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C4⋊C4C2×D411yescharacteristic
219C5×C4⋊C4C2×D412yes—
220C5×C4⋊C4C2×D412yes—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—21no—
232C42×C5—22no—
233C42×C5—22no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—21no—
237C42×C5—22no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5C2×D411yescharacteristic
242C42×C5C2×D411yescharacteristic
243C42×C5C2×D411yescharacteristic
244C42×C5C2411yescharacteristic
245#557C22×C511yescharacteristic
246#556—21no—
247#556C22×C511yescharacteristic
248#552—22no—
249#552—21no—
250D4×Q8C22×C511yescharacteristic
251#548—21no—
252#547—21no—
253#547C22×C511yescharacteristic
254#533—21no—
255#533C22×C511yescharacteristic
256C2×C4⋊Q8C22×C511yescharacteristic
257#529—21no—
258#529—22no—
259C4×#41—21no—
260C4×#41C22×C511yescharacteristic
261C4×#41C22×C511yescharacteristic
262C2×C4×Q8—21no—
263#491—22no—
264#487C22×C512yes—
265#487C22×C512yes—
266#477C22×C512yes—
267#477C22×C512yes—
268#476C22×C512yes—
269#476C22×C512yes—
270#475—21no—
271#475—21no—
272#474—21no—
273#474—21no—
274#428—21no—
275#428—21no—
276#423C22×C511yescharacteristic
277#423C22×C511yescharacteristic
278#419—22no—
279#417—21no—
280#417—21no—
281C4×M16C22×C511yescharacteristic
282#332C22×C512yes—
283#332C22×C512yes—
284Q8⋊C8C22×C512yes—
285Q8⋊C8C22×C512yes—
286D4⋊C8C22×C512yes—
287D4⋊C8C22×C512yes—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5#12011yescharacteristic
291C5×Q8—21no—
292C5×Q8—21no—
293C5×Q8—21no—
294C5×Q8—44no—
295C5×Q8—44no—
296C5×Q8—41no—
297C5×Q8—41no—
298C5×Q8—41no—
299C5×Q8—41no—
300C5×Q8—82no—
301C5×Q8#13712yes—
302C5×D4—21no—
303C5×D4—21no—
304C5×D4—21no—
305C5×D4—42no—
306C5×D4—42no—
307C5×D4—44no—
308C5×D4#13712yes—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—22no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—22no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—44no—
325C2×C4×C5—44no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—82no—
334C2×C4×C5#12011yescharacteristic
335C2×C4×C5#12011yescharacteristic
336C2×C4×C5#12011yescharacteristic
337C2×C4×C5C22×D411yescharacteristic
338C2×C4×C5C22×D411yescharacteristic
339C2×C4×C5C22×D411yescharacteristic
340C5×C8—42no—
341C5×C8—42no—
342C5×C8—42no—
343C2×#41—21no—
344C2×#41C5×D411yescharacteristic
345C2×#41C5×D411yescharacteristic
346C22×Q8—21no—
347C22×Q8—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C512yes—
357C4⋊Q8C23×C511yescharacteristic
358C4⋊Q8C23×C511yescharacteristic
359#126—22no—
360#126—22no—
361#126—22no—
362#125—22no—
363#125—22no—
364#125—21no—
365#125C5×D412yes—
366#124—22no—
367#124—21no—
368#123—22no—
369#123—22no—
370#123—22no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—21no—
378#121—22no—
379#121—21no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C5×D411yescharacteristic
388C4×Q8C5×D411yescharacteristic
389C4×Q8C23×C511yescharacteristic
390C4×Q8C23×C511yescharacteristic
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C5×D411yescharacteristic
399C4×D4C5×D411yescharacteristic
400C4×D4C23×C511yescharacteristic
401C4×D4C23×C511yescharacteristic
402#117—22no—
403#117—22no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117C5×D411yescharacteristic
408#117C5×D411yescharacteristic
409#117C5×D412yes—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C42—22no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C23×C511yescharacteristic
418#107—22no—
419#107—22no—
420#106—22no—
421#106—22no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8C23×C512yes—
425C4⋊C8C23×C512yes—
426#103—22no—
427#103—22no—
428#103—24no—
429#103—24no—
430#102—22no—
431#102—22no—
432#97—21no—
433C4×C8C23×C512yes—
434C22×C5—21no—
435C22×C5—21no—
436C22×C5—22no—
437C22×C5—21no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5C2×#12011yescharacteristic
444C4×C5—21no—
445C4×C5—21no—
446C4×C5—22no—
447C4×C5—21no—
448C4×C5—41no—
449C4×C5—41no—
450C4×C5—42no—
451C4×C5—42no—
452C4×C5—41no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—82no—
456C4×C5#45412yes—
457C4×C5C2×#13711yescharacteristic
458C4×C5C2×#13711yescharacteristic
459C4×C5#57511yescharacteristic
460C4×C5#57511yescharacteristic
461#41—22no—
462#41—22no—
463#41—41no—
464#41—41no—
465#41—42no—
466#41—42no—
467C2×Q8—22no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—22no—
471C2×Q8—44no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—41no—
475C2×Q8C2×C5×D411yescharacteristic
476C2×Q8C2×C5×D411yescharacteristic
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4C2×C5×D411yescharacteristic
481C2×D4C2×C5×D411yescharacteristic
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4C2×C5×D411yescharacteristic
492C22×C4C2×C5×D411yescharacteristic
493C22×C4C2×C5×D411yescharacteristic
494M16—42no—
495M16—42no—
496M16—42no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4C2×C5×D412yes—
519C4⋊C4C2×C5×D412yes—
520C4⋊C4C2×C5×D411yescharacteristic
521C4⋊C4C2×C5×D411yescharacteristic
522C4⋊C4C2×C5×D411yescharacteristic
523C4⋊C4C2×C5×D411yescharacteristic
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C42—22no—
536C42—22no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—22no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42C2×C5×D411yescharacteristic
545C42C2×C5×D411yescharacteristic
546C42C2×C5×D411yescharacteristic
547C42C24×C511yescharacteristic
548C2×C5—41no—
549C2×C5—42no—
550C2×C5—81no—
551C2×C5#300711yescharacteristic
552C2×C5#300711yescharacteristic
553C2×C5C2×#45411yescharacteristic
554C23—21no—
555C23—21no—
556C23C5×#12011yescharacteristic
557Q8—21no—
558Q8—21no—
559Q8—21no—
560Q8—44no—
561Q8—44no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—82no—
567Q8C5×#13712yes—
568D4—21no—
569D4—21no—
570D4—21no—
571D4—42no—
572D4—42no—
573D4—44no—
574D4C5×#13712yes—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—82no—
600C2×C4C5×#12011yescharacteristic
601C2×C4C5×#12011yescharacteristic
602C2×C4C5×#12011yescharacteristic
603C2×C4C22×C5×D411yescharacteristic
604C2×C4C22×C5×D411yescharacteristic
605C2×C4C22×C5×D411yescharacteristic
606C8—42no—
607C8—42no—
608C8—42no—
609C5#1853811yescharacteristic, direct product factor, Sylow
610C22—21no—
611C22—21no—
612C22—22no—
613C22—21no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22C2×C5×#12011yescharacteristic
620C4—21no—
621C4—21no—
622C4—22no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—82no—
632C4C5×#45412yes—
633C4C2×C5×#13711yescharacteristic
634C4C2×C5×#13711yescharacteristic
635C4C5×#57511yescharacteristic
636C4C5×#57511yescharacteristic
637C2—41no—
638C2—42no—
639C2—81no—
640C2C5×#300711yescharacteristic
641C2C5×#300711yescharacteristic
642C2C2×C5×#45411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3482C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C5×#3139C2semidirect
3. C5×#3079C2semidirect
4. C5×#3079C2semidirect
5. C5×#1638C2semidirect
6. C5×#1637C2semidirect
7. C5×#1636C2semidirect
8. C5×#1635C2semidirect
9. C5×#1561C2semidirect
10. C5×#1489C2semidirect
11. C5×#1489C2semidirect
55. #18538C5direct (N × H)
148. #3139C2×C5semidirect
149. #3079C2×C5semidirect
150. #3079C2×C5semidirect
151. #1638C2×C5semidirect
152. #1637C2×C5semidirect
153. #1636C2×C5semidirect
154. #1635C2×C5semidirect
155. #1561C2×C5semidirect
156. #1489C2×C5semidirect
157. #1489C2×C5semidirect
609. C5#18538direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#34822
C5×#31392
C5×#30792
C5×#16382
C5×#16372
C5×#16362
C5×#16352
C5×#15612
C5×#14892
#185385